Question

Giải bpt

x² - 4x - 21 > 0

Answer 1

\(x^2-4x-21>0\)

\(\Leftrightarrow\)  \(x^2-4x+4>25\)

\(\Leftrightarrow\) \(\left(x-2\right)^2>25\)

\(\Leftrightarrow\) \(\left|x-2\right|>5\)

\(\Leftrightarrow\orbr{\begin{cases}x-2>5\\x-2>-5\end{cases}\Leftrightarrow\orbr{\begin{cases}x>7\\x>-3\end{cases}}}\)

Answer 2

\(x^2-4x-21>0\)

\(x^2-4x+4-25>0\)

\(\left(x-2\right)^2>25\)

Ta có: \(25=5^2=\left(-5\right)^2\)

TH1: \(\left(x-2\right)^2>5^2\)

\(x-2>5\)

\(x>7\)

TH2: \(\left(x-2\right)^2>\left(-5\right)^2\)

\(x-2>-5\)

\(x>-3\)

Kết hợp cả 2 TH ta đc x>-3

=.= hok tốt!!